U.S. Sen. Kelly Ayotte said Sunday that "now that the Olympics are over, we need to watch the behavior of the Russians," and called on President Obama to pressure the Kremlin to stay out of the battle for control of the government in Ukraine.

The Ukrainian capital of Kiev has fallen to opposition forces; the country's parliament has voted to oust President Viktor Yanukovich, who had the backing of Vladimir Putin's Russian government.

A day after Yanukovich fled to the Russian-speaking east following dozens of deaths during street protests aimed at toppling him, parliament named new speaker Oleksander Turchinov as acting president. An ally of the ousted leader's long-jailed rival Yulia Tymoshenko, he aims to swear in a government by Tuesday that can provide authority until a presidential election on May 25.

The power struggle for control of the Ukrainian government is a battle between forces that want to align the country with the European Union to the west and efforts by Yanukovich and his allies, who have tried to deliver the country into the Russian sphere of influence to the east.

Turchinov said Sunday that while the newly installed Ukrainian regime wants improved relations with the Russians, Moscow must recognize the Ukraine's path toward "European integration" and must recognize "Ukraine's European choice."

Ayotte urged Obama to make it clear to Putin that Russia must not intervene in Ukrainian affairs.

"I believe the President needs to up his game and send a clear unequivocal public message to Putin not to interfere in what is happening in the Ukraine, to let the Ukrainian people determine their future," the New Hampshire Republican told Fox interviewers. "This is an opportunity for the President to really be unequivocal with Putin."

She said Russian interference in Ukrainian sovereignty could bring U.S. sanctions such as expansion of the 2012 Magnitsky Act. The act declared certain Russians persona non grata in the United States after the death of Serge Magnitsky, who died in prison after exposing corruption in the Putin government.

President Obama's national security adviser, Susan Rice, was asked on "Meet the Press" Sunday about the possibility of Russia sending troops to Ukraine, which Putin had hoped Yanukovich would keep closely allied to Moscow.

"That would be a grave mistake," Rice said. "It's not in the interests of Ukraine or of Russia or of Europe or the United States to see a country split. It's in nobody's interest to see violence return and the situation escalate."

Rice said President Obama had told Putin that the United States and Russia have a shared interest in keeping Ukraine unified and independent.

Ukraine depends on Russia for most of its natural gas and oil supplies. Russia has a naval base at Sebastopol in the Ukrainian province of Crimea.

Policy in tatters

Yanukovich's flight into hiding left Putin's Ukraine policy in tatters, on a day he had hoped eyes would be on the grand finale to the Sochi Olympics. The Kremlin leader spoke on Sunday with German Chancellor Angela Merkel, whose foreign minister had brokered a short-lived truce in Kiev on Friday.

They agreed Ukraine's "territorial integrity" must be maintained, Merkel's spokesman said in a statement.

British Foreign Secretary William Hague was asked if Russia might "send in the tanks" to defend its interests among ethnic Russians in the east and on the Crimea peninsula, where Moscow bases its Black Sea Fleet: "It would really not be in the interests of Russia to do any such thing," he told the BBC.

EU officials offered financial aid to the new government and to revive a trade deal that Yanukovich spurned under Russian pressure in November, sparking the protests that drove him from office after 82 deaths last week, many from police sniper fire.

In addition to any economic assistance the EU might offer, the U.S. has also promised help.

In Russia, where Putin had wanted Ukraine as a key part in a union of ex-Soviet states, the finance minister said the next installment of a $15-billion loan package agreed in December would not be paid, at least before a new government is formed.

Hectic voting

In a hectic round of voting in parliament, lawmakers rushed in some crowd-pleasing measures against the old administration, conscious that those still occupying Independence Square — or the Maidan — remain deeply suspicious of the political class.

They stripped Yanukovich of his abandoned country home near Kiev, complete with ostrich farm and hot tubs, its brash opulence fuelling demands that he be held to account for stealing taxpayer billions.

Turchinov said a government should be in place by Tuesday.

His ally, Tymoshenko, defeated by Yanukovich in a 2010 presidential election and was later jailed for corruption, ruled herself out as interim premier. Freed from a prison hospital on Saturday after more than two years in jail, she may want time to recover and build support before running for the presidency.

As prime minister following the largely peaceful Orange Revolution of 2004-05, which overturned a first presidential victory by Yanukovich, Tymoshenko disappointed many in Ukraine who had hoped for an end to the corruption and failed economic policies that marked the aftermath of Soviet communism.

"In these days the most important thing is to form a functioning government," said Vitaly Klitschko, a former world boxing champion and also a possible presidential contender.

On Independence Square, men were still wandering around with clubs and wearing homemade body armor, helmets and in some cases ski masks and camouflage fatigues.

"We'll stay here to the very end," said one, Bohdan Zakharchenko, 23, from Cherkasy, south of Kiev. "We will be here til there's a new president."